A Sufficient Condition for Global Optimality of Solutions to the Optimal Power Flow Problem

Recent applications of a semidefinite programming (SDP) relaxation to the optimal power flow (OPF) problem offers a polynomial time method to compute a global optimum for a large subclass of OPF problems. In contrast, prior OPF solution methods in the literature guarantee only local optimality for the solution produced. However, solvers employing SDP relaxation remain significantly slower than mature OPF solution codes. This letter seeks to combine the advantages of the two methods. In particular, we develop an SDP-inspired sufficient condition test for global optimality of a candidate OPF solution. This test may then be easily applied to a candidate solution generated by a traditional, only-guaranteed-locally-optimal OPF solver.